Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and angle β.

Triangle has two solutions: a=38.5; b=34.5; c=5.14552145419 and a=38.5; b=34.5; c=56.75217637256.

#1 Obtuse scalene triangle.

Sides: a = 38.5   b = 34.5   c = 5.14552145419

Area: T = 58.91444489058
Perimeter: p = 78.14552145419
Semiperimeter: s = 39.0732607271

Angle ∠ A = α = 138.4110608231° = 138°24'38″ = 2.41657208333 rad
Angle ∠ B = β = 36.5° = 36°30' = 0.6377045177 rad
Angle ∠ C = γ = 5.0899391769° = 5°5'22″ = 0.08988266433 rad

Height: ha = 3.06604908523
Height: hb = 3.41553303714
Height: hc = 22.90106772899

Median: ma = 15.42107365693
Median: mb = 21.37328593394
Median: mc = 36.46441151247

Inradius: r = 1.50878197495
Circumradius: R = 299.0002339927

Vertex coordinates: A[5.14552145419; 0] B[0; 0] C[30.94884891338; 22.90106772899]
Centroid: CG[12.03112345586; 7.63435590966]
Coordinates of the circumscribed circle: U[2.5732607271; 28.88659007729]
Coordinates of the inscribed circle: I[4.5732607271; 1.50878197495]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 41.5899391769° = 41°35'22″ = 2.41657208333 rad
∠ B' = β' = 143.5° = 143°30' = 0.6377045177 rad
∠ C' = γ' = 174.9110608231° = 174°54'38″ = 0.08988266433 rad




How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 38.5 ; ; b = 34.5 ; ; c = 5.15 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 38.5+34.5+5.15 = 78.15 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78.15 }{ 2 } = 39.07 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.07 * (39.07-38.5)(39.07-34.5)(39.07-5.15) } ; ; T = sqrt{ 3470.91 } = 58.91 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.91 }{ 38.5 } = 3.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.91 }{ 34.5 } = 3.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.91 }{ 5.15 } = 22.9 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 38.5**2-34.5**2-5.15**2 }{ 2 * 34.5 * 5.15 } ) = 138° 24'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 34.5**2-38.5**2-5.15**2 }{ 2 * 38.5 * 5.15 } ) = 36° 30' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.15**2-38.5**2-34.5**2 }{ 2 * 34.5 * 38.5 } ) = 5° 5'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.91 }{ 39.07 } = 1.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 38.5 }{ 2 * sin 138° 24'38" } = 29 ; ;





#2 Obtuse scalene triangle.

Sides: a = 38.5   b = 34.5   c = 56.75217637256

Area: T = 649.8276913357
Perimeter: p = 129.7521763726
Semiperimeter: s = 64.87658818628

Angle ∠ A = α = 41.5899391769° = 41°35'22″ = 0.72658718203 rad
Angle ∠ B = β = 36.5° = 36°30' = 0.6377045177 rad
Angle ∠ C = γ = 101.9110608231° = 101°54'38″ = 1.77986756563 rad

Height: ha = 33.75772422523
Height: hb = 37.6711125412
Height: hc = 22.90106772899

Median: ma = 42.83662445014
Median: mb = 45.32204572239
Median: mc = 23.04547245266

Inradius: r = 10.01664636641
Circumradius: R = 299.0002339927

Vertex coordinates: A[56.75217637256; 0] B[0; 0] C[30.94884891338; 22.90106772899]
Centroid: CG[29.23334176198; 7.63435590966]
Coordinates of the circumscribed circle: U[28.37658818628; -5.9855223483]
Coordinates of the inscribed circle: I[30.37658818628; 10.01664636641]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.4110608231° = 138°24'38″ = 0.72658718203 rad
∠ B' = β' = 143.5° = 143°30' = 0.6377045177 rad
∠ C' = γ' = 78.0899391769° = 78°5'22″ = 1.77986756563 rad

Calculate another triangle

How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 38.5 ; ; b = 34.5 ; ; c = 56.75 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 38.5+34.5+56.75 = 129.75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 129.75 }{ 2 } = 64.88 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 64.88 * (64.88-38.5)(64.88-34.5)(64.88-56.75) } ; ; T = sqrt{ 422275.02 } = 649.83 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 649.83 }{ 38.5 } = 33.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 649.83 }{ 34.5 } = 37.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 649.83 }{ 56.75 } = 22.9 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 38.5**2-34.5**2-56.75**2 }{ 2 * 34.5 * 56.75 } ) = 41° 35'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 34.5**2-38.5**2-56.75**2 }{ 2 * 38.5 * 56.75 } ) = 36° 30' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 56.75**2-38.5**2-34.5**2 }{ 2 * 34.5 * 38.5 } ) = 101° 54'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 649.83 }{ 64.88 } = 10.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 38.5 }{ 2 * sin 41° 35'22" } = 29 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.